A lunar month is twenty-nine and one half days, and 793 units, as we have explained.1 It is impossible for Rosh Chodesh to begin in the middle of the day - i.e., that a portion of the day would be part of the previous month and a portion of the day would be part of the following month - as [implied by Numbers 11:20]: "For a month of days...." According to the Oral Tradition,2 this was interpreted [to mean], "You count the days of a month; you do not count the hours [of a month]."

Therefore, some lunar months are established as lacking [a day], and others as full. A month that is lacking has only twenty- nine days, even though a lunar month is several hours longer. A full month is thirty days, even though a lunar month is several hours shorter. In this manner, the months will be calculated according to complete days, not according to hours.

If a lunar month were exactly twenty-nine and a half days [long], the years [would be divided evenly] into full and lacking months, and there would be exactly 354 days to a lunar year. Thus, there would be six full months and six lacking months. It is the units that exist in every month that exceed the half day - which ultimately add up to hours and days - that cause certain years to have more lacking months than full months, and other years to have more full months than lacking months.

According to this reckoning, the thirtieth day of the month is always established as Rosh Chodesh. If the month is lacking, the thirtieth day will be Rosh Chodesh of the coming month.

If the month is full [the coming month will have two days that are Rosh Chodesh]. The thirtieth day will be Rosh Chodesh, since a portion of it is [fit to be] Rosh Chodesh. [Nevertheless,] it will be counted as the completion of the previous month, which was full. The thirty-first day also will be Rosh Chodesh, and the reckoning [of the days of the coming month] will start from it. It is the day established [as Rosh Chodesh].

Thus, according to this calculation, there are some months that have only one day Rosh Chodesh, and other months that have two days Rosh Chodesh.

The following is the order of the full and lacking months according to [our] fixed calendar: Tishrei is always full. Tevet is always lacking. From Tevet on, there is one full month and one lacking month in sequence.

What is implied? Tevet is lacking; Shevat is full; Adar is lacking; Nisan is full; Iyar, lacking; Sivan, full; Tammuz, lacking; Av, full; Elul, lacking. In a leap year, the first Adar is full,3 and the second Adar is lacking.

Two months remain: Marcheshvan and Kislev. Sometimes they are [both] full; sometimes they are [both] lacking; and sometimes Marcheshvan is lacking and Kislev is full.

A year in which both of these months are full is called a year of complete months. A year in which both these months are lacking is called a year of lacking months. And a year in which Marcheshvan is full and Kislev is lacking is called a year whose months [proceed] in order.4

The way to know whether the months of a year will be lacking, will be complete, or will [proceed] in order [can be explained] as follows: First, determine the day on which Rosh HaShanah will fall in the year about whose months you desire to know, as explained in Chapter 7. Then determine the day on which Rosh HaShanah will fall in the year that follows.

Afterwards, count the number of days between them without including the day on which Rosh HaShanah falls in either of these years. If there are only two days between them,5 the months of the year will be lacking. If there are three days between them,6 the months of the year will proceed in order. And if there are four days between them,7 the months of the year will be complete.

When does the above apply? When the year in question is an ordinary year. When, however, [the year in question] is a leap year [different rules apply]: If there are only four days between the day on which [Rosh HaShanah] is established [in the leap year] and the day on which it will be established in the following year, the months of the year will be lacking.8 If there are five days between these [two days], the months of the year will proceed in order. And if there are six days between them, the months of the year will be complete.

What is implied? If we desire to know the order of the months of the present year, and [we know the following]: Rosh HaShanah falls on Thursday; it is an ordinary year; and in the following year Rosh HaShanah falls on Monday, there are three days between them and the months of the year proceed in order.9

If Rosh HaShanah falls on Tuesday in the following year, the months of the year will be complete.10 If Rosh HaShanah falls on the Sabbath in the present year, and on Tuesday in the following year, the months of the year will be lacking.11 Similar concepts should be applied regarding the calculation [of the order of the months] of a leap year, as was explained.

There are certain indications upon which one can rely, so that one will not err regarding the calculation of the order of the months of a year. These principles are based on the fundamental principles of the fixed calendar and the determination of the days on which Rosh HaShanah will be established and those that will cause it to be postponed, as we explained previously.

Whenever Rosh HaShanah is celebrated on a Tuesday, [the months of] the year will [proceed] in order. [This applies regardless of whether the year] is an ordinary year or a leap year.12

Whenever Rosh HaShanah is celebrated on the Sabbath or on a Monday, [the months of] the year will never [proceed] in order. [This applies regardless of whether the year] is an ordinary year or a leap year.13

[The following rules apply when] Rosh HaShanah falls on a Thursday. If the year is an ordinary year, it is impossible for its months to be lacking.14 If it is a leap year, it is impossible for its months to proceed in order.15

The Rambam gives examples in Halachah 9 to illustrate this situation and those that follow. When there are two days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and three days - i.e., 353 days - long.

When there are four days between the days on which Rosh HaShanah is celebrated in successive years, the year is 50 weeks and five days - i.e., 355 days - long. The remainder of an ordinary lunar year is slightly more than four days, producing a year whose months proceed in order. Frequently, however, the year will contain an extra day, if, because of the reasons mentioned in the previous chapter, the celebration of Rosh HaShanah is postponed. Similarly, it may lack a day, because the celebration of Rosh HaShanah was postponed in the previous year.

As mentioned, Rosh HaShanah cannot fall on Sunday, Wednesday, or Friday. Therefore, in an ordinary year, if Rosh HaShanah falls on a Tuesday, the following year it cannot fall on a Thursday, for then there would be only one day between them, producing a year of only 352 days. Nor can it fall on a Monday, for then the year would be 356 days long. Thus, the only day on which it can fall is the Sabbath, producing a year of 354 days. In such a year, the months proceed in order.

When Rosh HaShanah falls on Tuesday in a leap year, it cannot fall on Thursday or the Sabbath in the following year, for that would produce a year that is too short (380 or 382) days. Nor can it fall on Tuesday itself, for Rosh HaShanah falls on Tuesday only when the conjunction takes place not later than Tuesday, before noon. When the remainder of a leap year - 5 days, 21 hours, and 589 units - is added to noon time on Tuesday, the result is that the conjunction of the following year will take place on Sunday. Since Rosh HaShanah is never celebrated on Sunday, the holiday will be postponed until Monday. Thus, the length of the leap year will be 384 days, the length of a year whose months proceed in order.

For the months of an ordinary year to proceed in order, the year must be 354 days long. That means that if Rosh HaShanah fell on the Sabbath, it would have to fall on Wednesday in the following year, which is impossible. Similarly, if Rosh HaShanah fell on Monday, it would have to fall on Friday in the following year, which is also impossible.

For the months of a leap year to proceed in order, the year must be 384 days long. That means that if Rosh HaShanah had fallen on the Sabbath, in the following year it would have to fall on Friday, which is impossible. Similarly, if Rosh HaShanah had fallen on Monday, in the following year it would have to fall on Sunday, which is also impossible.

Moznaim is the publisher of the Nehardaa Shas, a new, state-of-the-art edition of the Talmud and all major commentaries in 20 volumes. Click here to purchase or email the publisher at sales@moznaim.com